Question

Simplify step by step


please thanks.

Answer 1

Hey there!

So, let's start out with figuring out the first part of this equation.


`\left[\begin{array}{ccc}\boxed{\boxed{4(x+2}}\end{array}\right]`

Step #1

Simplify
`(x+2)/(y2)`


`((4* ((x+2))/(x^2) +4x) \ +4`

Step #2


`( (4 \ * \ (x+2))/(x^2) )+ \ \ 4x)+4`

Step #3

We would have to rewrite this whole fraction using
`\boxed{(x^2)}` as the denominator.


`\boxed{\boxed{(4x= (4x)/(1) = (4x+x^2)/(x^2) )}}`

Step #4

We would have to combine the numerators.


`(4* \ (x+2) \ +4x \ * \ x^2)/(x^2)` =
`(4x^3 \ + \ 4x \ + \ 8)/(x^2)`

By finishing what is above, it would look like
`\swarrow \swarrow \swarrow \swarrow`


`((4x^3+4x+8)/(x^2) )`

Step #5

And now that we have come to know this from above, this leaves us with . . .


`4(x+2)/(x+2)(x+2)`

(Final answer)


`\left[\begin{array}{ccc}\boxed{\boxed{ (4)/(x)+2}} \end{array}\right]`

Hope this helps you!
~Jurgen

Answer 2

Hey there!

Normally, we would simplify the top using the distributive property which states that:

a(b + c) = ab + ac

However, we have a special situation here which makes the problem that much easier. Our first step is to take the denominator and put it in the form of a product of binomials. We know that we can use (x + 2)(x + 2) because when we use foil to solve this, we get x^2 + 2x + 2x + 4 = x^2 + 4x + 4

Therefore, we have:


`4(x+2)/(x+2)(x+2)`

Now, we can cancel one pair of (x+2) because (x+2)/(x+2) = 1

That gives us just that one four over the x + 2:


`4/x+2`

Hope this helps!